It is not clear whether the appealing correspondence between shallow trig network and GP with SE kernel can carry to the deep trigonometric network and 2-layer DGP discussed in this paper. Nevertheless, the perspective from neural tangent kernel [1]}, [2]} may shed some light on this issue. For gradient based learning of infinite and deep neural network \(f({\bf x}|\theta )\) , the network function shall eventually converge to the predictive mean of GP with the following kernel,
\(k({\bf x,y})=\operatorname{\mathbb {E}}_{\theta }\big [\frac{\partial f({\bf x}|\theta )}{\partial \theta }\cdot \frac{\partial f({\bf y}|\theta )}{\partial \theta }\big ]\:,\) 
